Hi Ryan,
We use "leak" when there is an unwanted and slow loss of liquid from a container.
Example: There is a leak in your car radiator. You have to get it fixed soon.
We also use "leak" to indicate a unintended disclosure of information.
Example: The leak of top secret information from government files set off a flurry.
When we have an unwanted substance (usually liquid) that gets into a place, we say that it "seeps" into that place.
Example: Water was seeping into the basement as the construction was shoddy.
Hope this helps.
Cheers,
Lance